This question is interesting, but difficult to give a full qualifying answer. Any way I will put my two cents here.
You can be a candidate if:
You are around here at least for one year and during that period you were constantly put effort to improve this community. Why one year? Each community works different. It will take some time to understand the community, how the community works here, what are the things we can do/no-do etc. So a buffer time of one year would take to understand the community in my opinion.
You are constantly moderating in community. There are lot of things come here. You are constantly monitoring the community activities and report any issues to moderators for immediate actions, taking actions against on false contents which you have privilege to do. Upvote questions and answers which are really relevant.
You are taking a humble approach to newbies. We are stable now. So we don't need to do a strict scrutiny to the new questions which are coming to our site now. We can take a humble approach now and teach a newbie how to ask a question and how to answer a question. This will enrich and inspire them and that will eventually leads to more frequent participation from their side. This is a must requirement in my opinion.
You have a quiet good knowledge about the moderation and your additional responsibilities if you become a moderator. For this, you should engage with the moderators and take feedback from them. Meta is a wonderful place to ask such questions if you are not clear with the approach you should take in a given situation or you need assistance from the moderators.
Last but not least, you are a person who are using all your moderation privileges in its fullest. This is a MUST.
You should not nominate if:
You just answered 5 questions and now you feel you know everything about moderation. We appreciate your effort, but which is not enough for moderation.
You don't have patience and you are responding to any no-do action with your first instinct or rage. Remember patience is the quality a moderator need. A best moderator will engage the community to take a decision if it is possible even if he can do that action with a simple click.
You don't know what are the rules in this community
You are not using your moderator privileges in it's fullest. Oh boy!! this is critical one.
Why I am not applying this time
If you look my profile, I am eligible to apply for election. But I am not considering me as an eligible candidate, since:
My moderation in this community for the past 5 month is very less. At least, it is not satisfying myself. I am not getting 2 hours to spend here due to my busy office work.
I know people who are constantly engaging with the community do exists and I would love to vote for them. Within two days, the people in my mind are not applying, then I will shoot a notification to them. This is something that I do always whenever an election happens.
Most importantly, I fear I could not find much time to do my moderation duties in the coming future. I think this is the reason why one of our existing moderator back out from his position. I really do appreciate that.
Now please keep this in mind and think. If you still feel you are good, then nominate yourself. :)